Taylor series-based transmission line equalization scheme

摘要

An equalization scheme for a transmission line employs a Taylor series expansion which enables the provided equalization to be adjusted based on line length. Multiple circuit blocks compute respective terms of the Taylor series, which are then summed to provide a compensating frequency response. For example, for a conductor having a frequency response given by H(f)=e^{−kl(1+j)√{square root over (f)}}, where k is a constant dependent on the physical parameters of the conductor, l is the length of the conductor and f is the frequency of the signal propagated via the conductor, the present scheme provides an inverse frequency response H⁻¹ (f) given by H⁻¹ (f)=; $$ 1+\frac{\mathrm{kl}\sqrt{f}}{1!}+\frac{k^2{l}^{2}f}{2!}+\frac{k^3{l}^3{f}^2}{3!}+\dots .$$The kl terms serve as weighting factors which vary with the length of the conductor.